Channel State Information at the Transmitter (CSIT) is crucial to the capacity performance and spatial multiplexing gain in downlink Broadcast Channel (BC), also called MU-MIMO, but having perfect CSIT is a challenging issue. Classically, in Frequency Division Duplexing (FDD), each user estimates their Channel State Information (CSI) in the specified subband using pilot and the estimated CSI is quantized and reported to the transmitter via a rate-limited link. In Time Division Duplexing (TDD), CSI is measured on the uplink and used in the downlink assuming channel reciprocity. Those CSI feedback mechanisms are subject to the estimation error and/or finite rate in the feedback link. Consequently, the transmitter obtains the CSI with imperfectness. Moreover, due to the frequency selectivity, constraints on uplink overhead and user distribution in the cell, the quality of CSI reported to the transmitter varies across users and subbands.
Specifically, the CSI quality patterns, formed by a user-frequency grid, can be generally illustrated as in FIG. 1. Considering an L-subband based two-user MISO-OFDMA framework, ajε[0,1] and bjε[0,1] respectively refer to the quality of the CSIT of user 1 100 and user 2 110 in subband j. For example, a1(120) is the quality of the CSIT of user 1 in subband 1 and b1(130) is the quality of the CSIT of user 2 in subband 2. “1” is equivalent to perfect CSIT as one stream/user can be successfully transmitted by simply performing Zero-Forcing Beamforming (ZFBF). “0” is equivalent to no CSIT because the imperfect CSIT cannot benefit the multiplexing gain when performing ZFBF. (More details about the definition of the quality parameters are presented in the next part.)
The performance is commonly evaluated in terms of (sum−)rate. At high SNR, the rate can be approximated by the multiplexing gain, also called Degrees-of-Freedom (DoF) hereafter. In the sequel we will look at DoF as the system performance metric. The DoF of user k writes as Math Figure 1.
MathFigure 1
                              d          k                =                              lim                          SNR              →              ∞                                ⁢                                    R              k                                      r              ⁢                                                          ⁢                              log                2                            ⁢              SNR                                                          [                  Math          .                                          ⁢          1                ]            
Where R_k is the rate achieved at user k in r subbands. DoF can be interpreted as the number of interference-free streams transmitted per subband at high SNR.
In such two-user BC, two fundamental transmission modes can be employed: 1) single-user transmission (one user is scheduled each time, like Frequency Division Multiple Access (FDMA)), also called SU-MIMO in LTE-Advanced, 2) conventional Multi-User MIMO (MU-MIMO) transmission (often relying on ZFBF or other filter designs like Signal to Leakage plus Noise Ratio SLNR). In FDMA (i.e, SU-MIMO), the transmitted signal in each subband only contains symbols intended for one user; In MU-MIMO (like ZFBF), the transmit signals contains message intended for several co-scheduled users. Considering a transmitter with two antennas and two users each with a single antenna, the transmitted signal in subband j with ZFBF writes as Math Figure 2.
MathFigure 2xj=ĝj⊥uj+ĥj⊥vj  [Math.2]
Where uj and vj are symbols intended for user 1 and user 2 respectively and

and

are respectively the CSIT of user 2 and user 1.

and

are respectively orthogonal to

and
.
The received signals, denoted as yj and zj at user 1 and user 2 respectively, write as Math Figure 3.
MathFigure 3yj=hjHĝj⊥uj+hjHĥj⊥vj+εj1 zj=gjHĝj⊥uj+gjHĥj⊥vj+εj2  [Math.3]
Where hj and gj are the CSI of user 1 and user 2 respectively,
εj1 
and
εj2 
are additive Gaussian noise.
SU-MIMO and MU-MIMO are major transmission strategies in WiMAX, LTE and LTE-A. SU-MIMO has been introduced in LTE Rel. 8 and MU-MIMO based on DM-RS and non-codebook based precoding (like ZFBF) has been introduced in Rel. 9 and further improved in Rel. 10. The major issue with MU-MIMO in current standards is that the transmission strategy has been designed under the assumption of perfect CSI knowledge at the transmitter but is actually used in scenarios are CSI is imperfectly known at the transmitter. This leads to major performance drops.
To see the disadvantage of FDMA (SU-MIMO) and ZFBF (MU-MIMO), let us evaluate their DoF performances in the following CSIT quality patterns.L=1, a1=1, a2=1
By performing ZFBF, each user will detect its own symbol without interference because the symbol intended for the other user is drowned by the noise. For instance, in yj, the received power of
hjH⊥vj 
is smaller than
εj1 
at high SNR. Hence, the sum DoF is 2.
By doing single-user transmission, since one user keeps silent, the active user receives one stream because each user has a single antenna. Hence, the sum DoF of 1.L=1,a1<1,b1<1
By performing ZFBF, the private symbols cannot be drowned by the noise at their unintended user, thus a rate loss will incur. For instance, the received power of
hjH⊥vj 
in yj scales higher than
εj1 
at high SNR and the rate of uj decreases. The sum DoF will be a function of the CSIT qualities, i.e. a1 and b1. When a1=b1=0, none of the user can decode its symbol. Hence, it is worth noting that when the CSIT is of very bad quality, performing ZFBF cannot achieve a DoF performance better than FDMA.L=2,a1=b2=1,b1=a2=0
By performing ZFBF in each subband, user 1 can decode u1 from y1 and user 2 can decode v2 from z2. However, user 1 and user 2 cannot decode their symbols respectively in subband 2 and subband 1. This is equivalence with performing FDMA in these two subbands. Specifically, user 1 (resp. user 2) is active in subband 1 (resp. subband 2) but silent in subband 2 (resp. subband 1). Consequently, this alternating CSIT state (a1=b2=1,b1=a2=0) does not boost the DoF performance if ZFBF is performed.